Using an imported model: Why does my mesh look like this?
The mesh imported did indeed use custom normals. The solution as posted worked perfectly:

You have Custom Split Normals Data added to the geometry, to fix this, while selecting the object, go to Data Tab in Properties Panel, scroll to find Geometry Data, and click Clear Custom Split Normals Data.
enter image description here
More information about this issue: Strange black shading. Cannot fully light mesh. (Cycles)